| Exam Board | Edexcel |
|---|---|
| Module | AEA (Advanced Extension Award) |
| Year | 2002 |
| Session | June |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Topic | Implicit equations and differentiation |
| Type | Find stationary points |
| Difficulty | Hard +2.3 This requires implicit differentiation to find dy/dx, setting it to zero to find stationary points, then solving the resulting system of equations (which involves substitution and solving a cubic). Finally, determining nature requires the second derivative via implicit differentiation again. The algebraic manipulation is substantial and the problem requires multiple sophisticated techniques in sequence, typical of challenging AEA questions. |
| Spec | 1.07n Stationary points: find maxima, minima using derivatives1.07p Points of inflection: using second derivative1.07s Parametric and implicit differentiation |
Find the coordinates of the stationary points of the curve with equation
$$x^3 + y^3 - 3xy = 48$$
and determine their nature.
[14]
\hfill \mbox{\textit{Edexcel AEA 2002 Q4 [14]}}